Dispersive Ones Research Articles

Some Exact Green Function Solutions for Non-Linear Classical Field Theories

We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones where the exact solution of the corresponding homogeneous equations can have some known shape. The technique has a formal similarity with the Dyson–Schwinger set of equations to solve quantum field theories. However, there are no physical constraints. Indeed, we show that a complete coincidence with the statistical field model of a quartic scalar theory can be achieved in the Gaussian expansion of the cumulants of the partition function.

Correlations of Surface Free Energy and Solubility Parameters with Dielectric Constant, Refractive Index, and Density for Liquids.

There should be some intrinsic correlations between the surface free energy (γ) and solubility (δ) parameters, called characteristic parameters here, of substances with their fundamental physical properties such as the refractive index (nD), relative dielectric constant (εr), and density (ρ) because they are all related to intermolecular interactions. Understanding the correlations between characteristic parameters and fundamental physical quantities is of great fundamental and practical importance. In the current work, possible relationships between the characteristic parameters (γ and δ) and the physical quantities (nD, εr, and ρ) were explored by a trial-and-error fitting method based on the data of 92 liquids (including 14 nonpolar, 37 polar, and 41 hydrogen-bonded liquids). The γ parameters include total (γt), dispersive (γd), and polar (γp) ones, and the δ parameters include the Hildebrand parameter (δt) and the Hansen-dispersive (δd), polar (δp), and hydrogen-bonded (δh) ones. For each characteristic parameter, its relationship with the physical quantities was established. The applicability of the so-obtained relationships was confirmed using the data of another 66 liquids as an external data set. The empirical relationships can be used to estimate the characteristic parameters of liquids from their easily measurable physical quantities.

A comparative study on microstructure and mechanical properties of wire-arc directed energy deposited Al–Zn–Mg–Cu alloy based on the cold metal transfer technology

Wire-arc directed energy deposition (DED) of Al–Zn–Mg–Cu alloy faced a tough challenge because of the occurrence of crack and pore defects caused by the high content of alloying elements. Three cold metal transfer (CMT) arc modes were studied to fabricate Al–Zn–Mg–Cu alloy components via the wire-arc DED process, with the aim of optimizing the deposition process and revealing the action mechanism of arc mode on the microstructure and mechanical properties. The effect of the CMT arc mode on the forming accuracy and arc/droplet behaviors was investigated with the assistance of the microscope and high-speed camera. The characteristics of grain morphology, crystallographic texture, and precipitated phase were quantitatively analyzed. The results show that the forming accuracies of deposited samples degenerate when using CMT and CMT pulse modes due to abnormal electrical waveforms and overflow/curve phenomenon. The finest grain size is realized under CMT advance mode because of its induced stirring effect on the molten pool, expanded constitutional supercooling zones, and extremely low heat input. The continuous and coarse precipitated phases in CMT and CMT pulse modes are transferred into dispersive ones in CMT advance mode. Moreover, the quantity and size of pores are also reduced in CMT advance mode. The combined action of microstructure optimization and defect reduction is conducive to improving the mechanical properties. Finally, the preferable ultimate tensile strength (∼278.15 MPa) and top elongation (∼6.50 %) of as-deposited Al–Zn–Mg–Cu alloy are achieved.

Isolated flat bands in 2D lattices based on a novel path-exchange symmetry

The increased ability to engineer two-dimensional (2D) systems, either using materials, photonic lattices, or cold atoms, has led to the search for 2D structures with interesting properties. One such property is the presence of flat bands. Typically, the presence of these requires long-ranged hoppings, fine-tuning of nearest neighbor hoppings, or breaking time-reversal symmetry by using a staggered flux distribution in the unit cell. We provide a prescription based on carrying out projections from a parent system to generate different flat band systems. We identify the conditions for maintaining the flatness and identify a path-exchange symmetry in such systems that cause the flat band to be degenerate with the other dispersive ones. Breaking this symmetry leads to lifting the degeneracy while still preserving the flatness of the band. This technique does not require changing the topology nor breaking time-reversal symmetry as was suggested earlier in the literature. The prescription also eliminates the need for any fine-tuning. Moreover, it is shown that the subsequent projected systems inherit the precise fine-tuning conditions that were discussed in the literature for similar systems, in order to have and isolate a flat band. As examples, we demonstrate the use of our prescription to arrive at the flat band conditions for popular systems like the Kagomé, the Lieb, and the Dice lattices. Finally, we are also able to show that a flat band exists in a recently proposed chiral spin-liquid state of the Kagomé lattice only if it is associated with a gauge field that produces a flux modulation of the Chern-Simons type.

Correlations of Surface Free Energy and Solubility Parameter with Dielectric Constant and Density for Inorganic Solids.

There should be some intrinsic correlations between the surface free energy (γ) and solubility (δ) parameters, called characteristic parameters here, of substances with their basic physical properties such as the relative dielectric constant (εr) and density (ρ), because they are all related to intermolecular interactions. Several correlations have been proposed empirically (or semiempirically) for liquids, but not for solids. It is essential to establish such correlations for solids because the estimation of γ and δ for solids is difficult and/or time-consuming. In the current work, the γ, δ, εr, and ρ data of 34 inorganic solids were chosen, and possible relationships between the characteristic parameters (γ and δ) and the physical quantities (εr and ρ) were explored by a trial-and-error fitting method based on the data of the solids. Six equations relating γ and δ to εr and δ were established. The γ parameters include total (γt), dispersive (γd), and polar (γp) ones, and the δ parameters include the Hildebrand parameter (δt) and the Hansen-dispersive (δd), polar (δp), and hydrogen-bonding (δh) ones. The empirical equations can be used to estimate the characteristic parameters of inorganic solids from their easily measurable physical quantities.

Agglomeration effect on biomechanical performance of CNT-reinforced dental implant using micromechanics-based approach

Dental implants have long played an important role in restoring lost teeth, but there are still concerns about their durability and long-term success. Commercial dental implants have traditionally been made of metallic and ceramic materials like titanium and zirconia; however, each kind of material has restrictions regarding osseointegration and mechanical characteristics that differ between native bone and the implant material, limiting the implant's longevity and reliability. To address these concerns, this research explores the use of carbon nanotubes (CNTs) in restorative dentistry, their excellent properties make them an ideal candidate for promoting bone growth around implanted device and ensuring long-lasting success. The objective of this study was to understand how CNT properties when incorporated into the titanium matrix may be able to better adapt to the oral environment taking into consideration the CNT agglomeration effects when designing reinforced nanocomposite materials for dental implant. A mathematical formulation of the micromechanics model was developed and improved to extend its application for the case of CNT-based composite materials for dental implants. A three dimensional (3D) model of bone structure around the osseointegrated dental implant was established considering different compositions of implant material. Finite Element Analysis (FEA) were conducted to assess the aggregation effect of implant incorporating CNTs into the titanium matrix, considering CNTs with both spherical inclusions (CNT clusters), and randomly dispersive ones (CNTs) in the titanium matrix, on osseointegration and bone remodeling around the dental implant and supporting bone system over a period of 48 months. Firstly, the effects of CNT-Ti implantation on time-dependent performance are evaluated in a computational remodeling framework. Then, Von Mises equivalent stresses are investigated to evaluate the stress distributions and micromotions in jaw bones of loaded implant with different composition of prosthetic material. Three agglomeration patterns are considered, particularly without agglomeration (ζ = ξ), partial and complete agglomeration (ζ < ξ, ξ = 1). Further, the influence of CNTs volume fraction variation is taken into account to predict the mechanical response of the bony system after CNT-reinforced dental implantation. It can be inferred that the agglomeration of CNTs reduces the elastic stiffness of the matrix. This is due to the fact that when CNTs are agglomerated, the inter-tube contacts are reduced and the effective stiffness of the matrix is decreased.

Theoretical Possibilities for Flat Band Superconductivity

One novel arena for designing superconductors with high $T_C$ is the flat-band systems. A basic idea is that flat bands, arising from quantum mechanical interference, give unique opportunities for enhancing $T_C$ with (i) many pair-scattering channels between the dispersive and flat bands, and (ii) an even more interesting situation when the flat band is topological and highly entangled. Here we compare two routes, which comprise a multi-band system with a flat band coexisting with dispersive ones, and a one-band case with a portion of the band being flat. Superconductivity can be induced in both cases when the flat band or portion is "incipient" (close to, but away from, the Fermi energy). Differences are, for the multi-band case, we can exploit large entanglement associated with topological states, while for the one-band case a transition between different (d and p) wave pairings can arise. These hint at some future directions.

Scaling laws for weakly disordered 1D flat bands

We investigate Anderson localization on various 1D structures having flat bands. The main focus is on the scaling laws obeyed by the localization length at weak disorder in the vicinity of flat-band energies. A careful distinction is made between situations where the scaling functions are universal (i.e. depend on the disorder distribution only through its width) and where they keep depending on the full shape of the disorder distribution, even in the weak-disorder scaling regime. Three examples are analyzed in detail. On the stub chain, one central flat band is isolated from two lateral dispersive ones. The localization length remains microscopic at weak disorder and exhibits disorder-specific features. On the pyrochlore ladder, the two flat bands are tangent to a dispersive one. The localization length diverges with exponent 1/2 and a non-universal scaling law, whose dependence on the disorder distribution is predicted analytically. On the diamond chain, a central flat band intersects two symmetric dispersive ones. The localization length exhibits two successive scaling regimes, diverging first with exponent 4/3 and a universal law, and then (i.e. further away from the pristine flat band) with exponent 1 and a non-universal law. Both scaling functions are also derived by analytical means.

Estimation of surface free energy and solubility parameters of Mg[sbnd]Al layered double hydroxides

The characteristic parameters, surface free energy (γ) and solubility parameters (δ), of Mg2AlNO3, Mg3AlNO3, Mg4AlNO3, Mg3AlCl, and Mg3AlCO3 layered double hydroxides (LDHs) were estimated using contact angle and liquid phase exfoliation (LPE) methods. The γ parameters include total (γst), dispersive (γsd), and polar (γsp) ones. The δ parameters include the Hildebrand parameter (δt,s) and the Hansen dispersive (δd,s), polar (δp,s), and hydrogen-bonding (δh,s) ones. Results show that the γst, γsd, and γsp of the five LDHs are ∼50.9–56.9, 35.2–39.4, and 15.6–18.8 mJ/m2, respectively, and the δt,s, δd,s, δp,s and δh,s of the LDHs except for the Mg3AlCO3 LDH are ∼31.4–32.9, 17.2, 9.5–10.0, and 24.5–26.1 MPa1/2, respectively. The compositions of LDHs have no obvious impact on all the characteristic parameters. In comparison with van de Waals attraction-bonded materials, the electrostatic attraction-bonded LDHs exhibit higher γst and δt,s values and, especially, much larger δh,s values. The characteristic parameter matching principle and the mixed-solvent strategy are suitable for the LPE of LDHs. Non-toxic glycol/PEG200 mixed liquids are found to be a good medium for the direct LPE of LDHs, producing monolayer nanosheets. To the best of our knowledge, this is the first report on the γ and δ parameters of LDHs. This work not only deepens the understanding of the feature of LDHs, but also provides effective liquid media for the direct LPE of LDHs.

Correlations of surface free energy and solubility parameters for solid substances

HypothesisBoth the surface free energy (γ) and solubility (δ) parameters of substances are related to their cohesive energies which are decided by intermolecular interactions, and there should be some intrinsic relationships between the two parameters. Understanding of the γ–δ correlations is of great fundamental and practical importance. Several empirical γ–δ equations have been proposed so far, but their application to solids is limited. This is because the molar volume (V~) as a parameter exists in these equations while the V~ of solids is commonly hard to be obtained. Hence, the development of γ–δ equations without the parameter V~ is essential for solids. MethodThe γ and δ data of 21 solids including polymers and layered solid materials were chosen, and possible γ–δ relationships were systematically explored using the parameter data of solids by a trial and error fitting method. FindingSix γ–δ equations without the parameter V~ are proposed. The γ parameters include total (γt), dispersive (γd), and polar (γp) ones, and the δ parameters include the Hildebrand parameter (δt) and the Hansen dispersive (δd), polar (δp), and hydrogen-bonding (δh) ones. Interestingly, the so-obtained V~-free γ–δ equations are also valid for most liquids including nonpolar and polar ones. These γ–δ equations can provide a way to estimate non-measurable parameters from measurable parameters for solid materials, which is beneficial to the application of the characteristic parameters (γ and δ) for solid material engineering.

Two-phonon Raman bands of single-walled carbon nanotubes: A case study

It has been long accepted that the second-order Raman bands in carbon nanotubes are enhanced through the double-resonance mechanism. Although separate aspects of this mechanism have been studied for a few second-order Raman bands, including the most intense defect-induced D band and the two-phonon 2D band, a complete computational approach to the second-order bands is still lacking. Here, we propose such an approach, entirely based on a symmetry-adapted nonorthogonal tight-binding model with ab initio derived parameters. As a case study, we consider a nanotube $(6,5)$, for which we calculate the two-phonon spectrum. We investigate in detail the 2D band and identify three contributions to it: a nondispersive one and two dispersive ones, which are found to depend on the electron and phonon dispersion of the nanotube, and on the laser excitation. We also predict two-phonon bands, which are not allowed in the parent structure graphene. The obtained two-phonon bands are in very good agreement with the available experimental data. The symmetry-adapted formalism makes feasible the calculation of the two-phonon Raman bands of any observable nanotube.

A Critical Review on Filter Design Criteria for Dispersive Base Soils

Dispersive soils have become common materials for the construction industry. Highly susceptible to internal erosion and piping, dispersive soils must only be used with specific engineering measure in order to avoid failures that were often catastrophic. In an earth dam, clayey soils are used for the core and sandy materials are used for the filter to retain the eroded core soils and prevent their migration. In the absence of first-rate core material, dispersive soils have been used instead. This paper provides a review of the current knowledge and experiences regarding filtration of core soils, particularly the dispersive ones. The engineering problems associated with the use of dispersive soils are discussed and significant findings from previous studies on protective filters are summarized. It is worthy to note that the current review considers both, the conventional, rather empirical filter design criteria based on particle sizes and the current, quite theoretical state-of-the-art filter design criteria based on constriction sizes, with discussion given on the advantages and disadvantages of both. The information provided by this review should be handy for the study, design, construction, and operation of related geotechnical and geo-environmental projects.

New class of flat-band models on tetragonal and hexagonal lattices: Gapped versus crossing flat bands

There is an increasing fascination centered on superconductivity and topological properties with bands that are flat due to quantum mechanical interference. An important question remains: can we actually control the energy of the flat band against the dispersive ones? Here, the authors have constructed classes of models in two (or higher) dimensions in a systematic extension of the known flat bands, where the controllability provides a flat band with a tunable gap, or a flat band that pierces right through the dispersive one. While the former may favor ferromagnetism, the latter is expected to favor high-${T}_{c}$ superconductivity through virtual pair hopping from dispersive to flat bands.

A Fourier transform Raman spectrometer with visible laser excitation

We present the development and performance of a Fourier transformation (FT)‐based Raman spectrometer working with visible laser (532 nm) excitation. It is generally thought that FT‐Raman spectrometers are not viable in the visible range where shot noise limits the detector performance and therein they are outperformed by grating based, dispersive ones. We show that contrary to this common belief, the recent advances of high‐performance interference filters makes the FT‐Raman design a valid alternative to dispersive Raman spectrometers for samples which do not luminesce. We critically compare the performance of our spectrometer to two dispersive ones: a home‐built single channel and a state‐of‐the‐art charge coupled device‐based instruments. We demonstrate a similar or even better sensitivity than the charge coupled device‐based dispersive spectrometer particularly when the laser power density is considered. The instrument possesses all the known advantages of the FT principle of spectral accuracy, high throughput, and economic design. We also discuss the general considerations, which helps the community reassess the utility of the different Raman spectrometer designs. Copyright © 2015 John Wiley &amp; Sons, Ltd.

DISCRIMINATING THE FREQUENCY DISPERSIVE SCATTERING CENTERS OF COMPLEX TARGETS BY WIDEBAND GROUP DELAY ANALYSIS

Waveguide geometry is one of the most critical frequency Dispersive Scattering Centres (DSCs) in actual complex radar targets. Because of the occurrence of nonlinear dispersive scattering phase or range extension phenomena the nearby scatterers may be hidden in such cases. So, degradation of spatial resolution occurs in corresponding range profiles. According to a relatively simple parametric scattering model, a computationally efficient technique is introduced to analyze the complex range profiles including both backscattering field intensity and phase. The group delay of each scatterer is used as a criterion for discriminating the dispersive and non-dispersive ones. The wideband measured data samples are used for evaluating the technique, and the comparison is performed relative to Fourier- based results.

Landscape structure and genetic architecture jointly impact rates of niche evolution

Evolutionary adaptation is a key driver of species' range dynamics. Understanding the factors that affect rates of adaptation at range margins is thus crucial for interpreting and predicting changes in species' ranges. The spatial structure of environmental conditions is one of the determinants of whether and how quickly adaptations occur. However, while landscape structures at range edges are typically complex, most theoretical work has so far focused on relatively simple environmental geometries.Using an individual‐based allelic model, we explore the effects of different landscape structures on the rate of adaptation to novel environments and investigate how these structures interact with the genetic architecture of the trait governing adaptation and the dispersal capacity of the considered species. Generally, we find that rapid adaptation is favored by a good match between the coarseness of the trait's genetic architecture (many loci of small effects versus few loci of large effects) and the coarseness of the landscape (abruptness of transitions in environmental conditions). For example, in rugged landscapes, adaptation is quicker for genetic architectures with few loci of large effects, while for shallow gradients the opposite is true. Moreover, dispersal capacities affect the rate of adaptation by modulating the ‘apparent coarseness’ of the landscape: a gradient perceived as smooth by species with limited dispersal capacities appears rather steep for highly dispersive ones. We also find that the distribution of evolving phenotypes strongly depends on the interplay of landscape structure and dispersal capacities, ranging from two distinct phenotypes for most rugged landscapes, over the co‐occurrence of an additional third phenotype for highly dispersive species, to the whole range of phenotypes on smooth gradients.By identifying basic factors that drive the fixation probability of newly arising beneficial mutations, we hope to further broaden the understanding of evolutionary adaptation at range margins and, hence, species' range dynamics.

Influence of nanostructured ZrO2 additions on the wear resistance of Ni-based alloy coatings deposited by APS process

In the present investigation, the influence of the addition of nanostructure zirconia particles on the microstructure, micro-hardness and wear performance of a Ni-based alloy (Colmonoy 88) deposited by atmospheric plasma spraying (APS) on low carbon steel has been reported. Two different procedures were tested: (i) spraying powders of Colmonoy 88 and zirconia mixed by mechanical alloying and (ii) spraying powders separately using a dual powder injection system available at the APS equipment. The microstructure and the mechanical properties of coatings were characterized by scanning electron microscopy/energy dispersive X-ray analysis (SEM-EDS), X-ray diffraction (XRD) and micro-hardness measurements. The tribological properties were evaluated at room temperature in reciprocating sliding wear equipment. The results indicate that the as-sprayed modified coatings were mainly composed by Ni, Ni–Cr–Fe, Cr23C6, Cr5B3, and tetragonal zirconia. Evenly distribution of zirconia can be seen in the coatings produced by powders prepared by mechanical alloying, while dispersive ones can be seen in the other case. Hardness and wear resistance of coatings is increased with nanostructured zirconia additions, while their friction coefficient is decreased. Coatings produced with mechanical alloying show the highest wear resistance of all tested coatings. Nanostructured ZrO2 coating displays the worst wear resistance.

The Research of Chemical Plating of Pd/Sn on Graphite Anode Surface and its Electro-Catalytic Properties

The Pd/Sn catalytic coating on graphite electrode had been synthesized by chemical plating in this paper. Scanning electron microscope(SEM)and Electrochemical workstation(EW)were used to analyze the coating surface topography and electro-catalytic properties of modified graphite electrode with and without the coating. Results show that Pd and Sn are in the form of spherical particle and completely cover the surface of graphite electrode includes concave defects. Most Pd and Sn particles are dispersive ones of size of about 70 nm and few of which are polymerized in island forms. The peak value of current density increases with scanning speed, which goes positive potential scanning. Further more, the peak current increases with the concentration of NaOH solution, which shows nonlinear relationship between peak current and solution concentration, The peak current increases more rapidly with solution concentration increases in low NaOH concentration solution than that in high NaOH concentration solution.

Well-Posedness of Strongly Dispersive Two-Dimensional Surface Wave Boussinesq Systems

We consider in this paper the well-posedness for the Cauchy problem associated with two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. We emphasize the case of the strongly dispersive ones with focus on the “KdV-KdV” system which possesses the strongest dispersive properties and which is a vector two-dimensional extension of the classical KdV equation.

Manufacturing expedients in medieval ceramics in Apulia

Abstract A group of 51 shards of medieval polychrome glazed pottery, coming from Canosa castle archaeological site (Bari, Italy), has been investigated through surface analytical techniques, such as Scanning Electron Microscopy (SEM) with Energy Dispersive X-ray Spectroscopy (EDS) and elemental ones, such as Inductively Coupled Plasma–Optical Emission Spectroscopy (ICP–OES) and Absorption Atomic Spectroscopy (AAS) by flame and electro-thermal atomisation. The investigation was aimed at defining the elemental composition of pottery findings, identifying pigments and clarifying glaze types. The results of the analytical characterization allowed the identification of materials and technological expedients used for pottery manufacturing, highlighting original features in the production of the investigated pottery. The quantitative analysis performed on ceramic paste, glaze and painted decorations provided a significant number of results, thus enabling their effective exploitation for multivariate statistical techniques, in order to find out possible groups of pottery items with defined similarity within the samples.